A Minimal Completion of Doubly Substochastic Matrix

Authors

Lei Cao, Georgian Court UniversityFollow
Selcuk Koyuncu, University of North Georgia
Timmothy Parmer, University of North Georgia

Document Type

Article

Publication Date

11-2016

Publication Title

Linear and Multilinear Algebra

Keywords

Doubly stochastic matrices, Doubly substochastic matrices, Birkhoff's theorem, Permutation matrices

ISSN

0308-1087

Volume

64

Issue/No.

11

First Page

2313

Last Page

2334

Abstract

Let B be an n x n doubly substochastic matrix and let s be the sum of all entries of B. In this paper, we show that B has a sub-defect of k, which can be computed by taking the ceiling of n - s, if and only if there exists an (n + k) x (n + k) doubly stochastic extension containing B as a submatrix and k minimal. We also propose a procedure constructing a minimal completion of B, and then express it as a convex combination of partial permutation matrices.

Comments

©2016 Taylor & Francis

NSUWorks Citation

Cao, Lei; Koyuncu, Selcuk; and Parmer, Timmothy, "A Minimal Completion of Doubly Substochastic Matrix" (2016). Mathematics Faculty Articles. 270.
https://nsuworks.nova.edu/math_facarticles/270

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1080/03081087.2016.1155531